Water Damage, continues to turn on and off

I read through all of the iphone 5s water fixes, but couldn't find this one. Here is what I have done.

My phone was in a lifeproof case, but I forgot to check the seals and it floated down the river for 45mins (it was really lucky I even found it). It was dead when I found it.

1.) I started with rice, and then switched to silica gel once I was able to get it. When the phone was plugged in it turned on to the apple screen and off continually. I could put the phone into dfu mode, but didn't restore it.

2.) I ordered a new battery, soaked all of the parts in ISO alcohol, and then cleaned them to the best of my ability.

3.) I replaced the battery, and my phone came back to life. I backed it up, and was getting ready to go get a new SIM.

4.) However, then I noticed the battery life was terrible, (6hours in airplane mode).

5.) Now all it does is power cycle when plugged in again, i.e. turn on to apple logo and off while plugged in.

Any ideas on what to do next? Could it just be a bad battery (got it from here), or is my phone toast?